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Section: Application Domains

Hydrological disasters

It is a violent, sudden and destructive flow. Between 1996 and 2005, nearly 80$\%$ of natural disasters in the world have meteorological or hydrological origines. The main interest of their study is to predict the areas in which they may occur most probably and to prevent the damages by means of suitable amenities. In France, floods are the most recurring natural disasters and produce the worse damages. In addition, it can be a cause or a consequence of a dam break. The large surface they cover and the long period they can last requires the use of reduced models like the shallow water equations. In urban areas, the flow can be largely impacted by the debris, in particular cars, and required fluid/structure interactions to be well understood. Moreover, underground flows, in particular in sewer, can accelerate and amplify the flow. To take them into account, the model and the numerical resolution should be able to treat the transition between free surface and underground flows.

Tsunamis are another hydrological disaster largely studied. Even if the propagation of the wave is globally well described by the shallow water model in oceans, it is not the case close to the epicenter and in the coastal zone where the bathymetry leads a vertical accretion and produce substantial dispersive effects. The non-hydrostatic terms have to be considered and an efficient numerical resolution should be induced.

Whereas the viscous effects can often be neglected in water flows, they have to be taken into account in situations such as avalanches, debris flows, pyroclastic flows, erosion processes,...i.e. when the fluid rheology becomes more complex. Gravity driven granular flows consist of solid particles commonly mixed with an interstitial lighter fluid (liquid or gas) that may interact with the grains and decrease the intensity of their contacts, thus reducing energy dissipation and favoring propagation. Examples include subaerial or subaqueous rock avalanches (e.g. landslides).